ISO/IEC Guide 98-3:2008/Suppl 2:2011

Extension to any number of output quantities

Price from:
€ 165.29


This Supplement to the \Guide to the expression of uncertainty in measurement" (GUM) is concerned with
measurement models having any number of input quantities (as in the GUM and GUM Supplement 1) and any
number of output quantities. The model and quantities involved might be real or complex. Two approaches are
considered for treating such models. The first approach is a generalization of the GUM uncertainty framework.
The second is a Monte Carlo method as an implementation of the propagation of distributions. In cases where
the applicability of the GUM uncertainty framework is questionable, appropriate use of the Monte Carlo method
would be expected to provide valid results.
The approach based on the GUM uncertainty framework is applicable when the input quantities are summa-
rized (as in the GUM) in terms of estimates and standard uncertainties associated with these estimates and,
when appropriate, covariances associated with pairs of these estimates. Formulae and procedures are provided
for obtaining estimates of the output quantities and for evaluating the associated standard uncertainties and
covariances. Variants of the formulae and procedures relate to models for which the output quantities (a) can
be expressed directly in terms of the input quantities as measurement functions, and (b) are obtained through
solving a measurement model (which links indirectly the input and output quantities).
The counterparts of the formulae in the GUM for the standard uncertainty associated with an estimate of
the output quantity would be algebraically cumbersome. Such formulae are provided in a more compact form
in terms of matrices and vectors, the elements of which contain variances (squared standard uncertainties),
covariances and sensitivity coeficients. An advantage of this form of presentation is that these formulae can
readily be implemented in the many computer languages and systems that support matrix algebra.
The Monte Carlo method is based on (i) the assignment of probability distributions to the input quantities
in the model [JCGM 101:2008 6], (ii) the determination of a discrete representation of the (joint) probability
distribution for the output quantities, and (iii) the determination from this discrete representation of estimates
of the output quantities and the evaluation of the associated standard uncertainties and covariances. This
approach constitutes a generalization of the Monte Carlo method in Supplement 1 to the GUM, which applies
to a single scalar output quantity.
For a prescribed coverage probability, this Supplement can be used to provide a coverage region for the output
quantities of a multivariate model, the counterpart of a coverage interval for a single scalar output quantity.
The provision of coverage regions is limited to those taking the form of a hyper-ellipse or a hyper-rectangle.
These coverage regions are produced from the results of the two approaches described here.
This Supplement contains detailed examples to illustrate the guidance provided.
This document is a Supplement to the GUM and is to be used in conjunction with it and GUM Supplement 1.
The audience of this Supplement is that of the GUM and GUM Supplement 1.

Number of pages: 0

Published: 2011-11-09

International relationships :

ICS: 17.020 - Metrology and measurement in general

Item number: M225577